Ta có: \(AB=AC\Rightarrow\Delta ABC\) cân tại A\(\Rightarrow\widehat{ABC}=\widehat{ACB}\)
Theo gt: \(AB=AC;AD=AE\Rightarrow AB-AD=AC-AE\Rightarrow DB=CE\)
Xét \(\Delta DBC\) và \(\Delta ECB\) có:
BC cạnh chung
\(\widehat{ABC}=\widehat{ACB}\)
\(DB=CE\left(cmt\right)\)
\(\Rightarrow\Delta DBC=\Delta ECB\left(c-g-c\right)\)
\(\Rightarrow CD=BE\) (2 cạnh tương ứng)
b. Ta có: \(\widehat{ABC}=\widehat{ACB};\widehat{EBC}=\widehat{ACB}\left(\Delta DBC=\Delta ECB\right)\)
\(\Rightarrow\widehat{ABC}-\widehat{EBC}=\widehat{ACB}-\widehat{DCB}\Rightarrow\widehat{ABO}=\widehat{ECO}\)
Theo cmt: \(\Delta DBC=\Delta ECB\Rightarrow\widehat{BDO}=\widehat{CEO}\) ( 2 góc tương ứng)
Xét \(\Delta BOD\) và \(\Delta COE\) có:
\(\widehat{BDO}=\widehat{CEO}\left(cmt\right)\)
\(AB=CE\left(cmt\right)\)
\(\widehat{DBO}=\widehat{ECO}\left(cmt\right)\)
\(\Rightarrow\Delta BOD=\Delta COE\left(g-c-g\right)\)
